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A Graphical Approach to College Algebra

John Hornsby,Margaret L. Lial,Gary Rockswold

Chapter 2

Analysis of Graphs of Functions - all with Video Answers

Educators

AG

Section 1

Graphs of Basic Functions and Relations; Symmetry

00:24

Problem 1

Fill in each blank with the correct response. Do not use a calculator.
The domain and the range of the identity function are both______.

AG
Ankit Gupta
Numerade Educator
00:13

Problem 2

Fill in each blank with the correct response. Do not use a calculator.
The domain of the squaring function is ________ , and its range is _______.

AG
Ankit Gupta
Numerade Educator
00:11

Problem 3

Fill in each blank with the correct response. Do not use a calculator.
The graph of the cubing function changes from "opening downward" to "opening upward" at the point _______.

AG
Ankit Gupta
Numerade Educator
00:19

Problem 4

Fill in each blank with the correct response. Do not use a calculator.
The domain of the square root function is _______ and its range is _______.

AG
Ankit Gupta
Numerade Educator
00:10

Problem 5

Fill in each blank with the correct response. Do not use a calculator.
The cube root function _________ on its entire domain. (increases/decreases)

AG
Ankit Gupta
Numerade Educator
00:20

Problem 6

Fill in each blank with the correct response. Do not use a calculator.
The largest open interval that the absolute value function decreases on is _______ and the largest open interval that it increases on is ________.

AG
Ankit Gupta
Numerade Educator
00:26

Problem 7

The graph of the relation $x=y^{2}$ is symmetric with respect to the ______.

AG
Ankit Gupta
Numerade Educator
00:41

Problem 8

Fill in each blank with the correct response. Do not use a calculator.
The function $f(x)=x^{4}+x^{2}$ is an ______ function. (even/odd)

AG
Ankit Gupta
Numerade Educator
00:53

Problem 9

Fill in each blank with the correct response. Do not use a calculator.
The function $f(x)=x^{3}+x$ is an _______ function. (even/odd)

AG
Ankit Gupta
Numerade Educator
00:18

Problem 10

Fill in each blank with the correct response. Do not use a calculator.
If a function is even, its graph is symmetric with respect to the _______ If it is odd, its graph is symmetric with respect to the ______.

AG
Ankit Gupta
Numerade Educator
00:59

Problem 11

Determine the largest intervals of the domain over which each function is continuous.
(GRAPH CAN NOT COPY)

AG
Ankit Gupta
Numerade Educator
01:05

Problem 12

Determine the largest intervals of the domain over which each function is continuous.
(GRAPH CAN NOT COPY)

AG
Ankit Gupta
Numerade Educator
00:51

Problem 13

Determine the largest intervals of the domain over which each function is continuous.
(GRAPH CAN NOT COPY)

AG
Ankit Gupta
Numerade Educator
00:51

Problem 14

Determine the largest intervals of the domain over which each function is continuous.
(GRAPH CAN NOT COPY)

AG
Ankit Gupta
Numerade Educator
00:49

Problem 15

Determine the largest intervals of the domain over which each function is continuous.
(GRAPH CAN NOT COPY)

AG
Ankit Gupta
Numerade Educator
02:26

Problem 16

Determine the largest intervals of the domain over which each function is continuous.
(GRAPH CAN NOT COPY)

AG
Ankit Gupta
Numerade Educator
05:28

Problem 17

Determine the largest open intervals of the domain over which each function is (a) increasing, (b) decreasing, and (c) constant. Then give the (d) domain and (e) range.
(GRAPH CAN NOT COPY)

AG
Ankit Gupta
Numerade Educator
07:25

Problem 18

Determine the largest open intervals of the domain over which each function is (a) increasing, (b) decreasing, and (c) constant. Then give the (d) domain and (e) range.
(GRAPH CAN NOT COPY)

AG
Ankit Gupta
Numerade Educator
06:21

Problem 19

Determine the largest open intervals of the domain over which each function is (a) increasing, (b) decreasing, and (c) constant. Then give the (d) domain and (e) range.
(GRAPH CAN NOT COPY)

AG
Ankit Gupta
Numerade Educator
05:38

Problem 20

Determine the largest open intervals of the domain over which each function is (a) increasing, (b) decreasing, and (c) constant. Then give the (d) domain and (e) range.
(GRAPH CAN NOT COPY)

AG
Ankit Gupta
Numerade Educator
09:13

Problem 21

Determine the largest open intervals of the domain over which each function is (a) increasing, (b) decreasing, and (c) constant. Then give the (d) domain and (e) range.
(GRAPH CAN NOT COPY)

AG
Ankit Gupta
Numerade Educator
09:15

Problem 22

Determine the largest open intervals of the domain over which each function is (a) increasing, (b) decreasing, and (c) constant. Then give the (d) domain and (e) range.
(GRAPH CAN NOT COPY)

AG
Ankit Gupta
Numerade Educator
03:55

Problem 23

Graph each function in the standard viewing window of your calculator, and trace from left to right along a representative portion of the specified interval. Then fill in the blank of the following sentence with either increasing or decreasing.
Over the interval specified, this function is __________.

$$f(x)=x^{5} ;(-\infty, \infty)$$

AG
Ankit Gupta
Numerade Educator
03:33

Problem 24

Graph each function in the standard viewing window of your calculator, and trace from left to right along a representative portion of the specified interval. Then fill in the blank of the following sentence with either increasing or decreasing.
Over the interval specified, this function is __________.

$$f(x)=-x^{3} ;(-\infty, \infty)$$

AG
Ankit Gupta
Numerade Educator
03:11

Problem 25

Graph each function in the standard viewing window of your calculator, and trace from left to right along a representative portion of the specified interval. Then fill in the blank of the following sentence with either increasing or decreasing.
Over the interval specified, this function is __________.

$$f(x)=x^{4} ;(-\infty, 0)$$

AG
Ankit Gupta
Numerade Educator
00:46

Problem 26

Graph each function in the standard viewing window of your calculator, and trace from left to right along a representative portion of the specified interval. Then fill in the blank of the following sentence with either increasing or decreasing.
Over the interval specified, this function is __________.

$$f(x)=x^{4} ;(0, \infty)$$

AG
Ankit Gupta
Numerade Educator
01:02

Problem 27

Graph each function in the standard viewing window of your calculator, and trace from left to right along a representative portion of the specified interval. Then fill in the blank of the following sentence with either increasing or decreasing.
Over the interval specified, this function is __________.

$$f(x)=-|x| ;(-\infty, 0)$$

AG
Ankit Gupta
Numerade Educator
00:50

Problem 28

Graph each function in the standard viewing window of your calculator, and trace from left to right along a representative portion of the specified interval. Then fill in the blank of the following sentence with either increasing or decreasing.
Over the interval specified, this function is __________.

$$f(x)=-|x| ;(0, \infty)$$

AG
Ankit Gupta
Numerade Educator
00:44

Problem 29

Graph each function in the standard viewing window of your calculator, and trace from left to right along a representative portion of the specified interval. Then fill in the blank of the following sentence with either increasing or decreasing.
Over the interval specified, this function is __________.

$$f(x)=-\sqrt[3]{x} ;(-\infty, \infty)$$

AG
Ankit Gupta
Numerade Educator
00:44

Problem 30

Graph each function in the standard viewing window of your calculator, and trace from left to right along a representative portion of the specified interval. Then fill in the blank of the following sentence with either increasing or decreasing.
Over the interval specified, this function is __________.

$$f(x)=-\sqrt{x} ;(0, \infty)$$

AG
Ankit Gupta
Numerade Educator
01:00

Problem 31

Graph each function in the standard viewing window of your calculator, and trace from left to right along a representative portion of the specified interval. Then fill in the blank of the following sentence with either increasing or decreasing.
Over the interval specified, this function is __________.

$$f(x)=1-x^{3} ;(-\infty, \infty)$$

AG
Ankit Gupta
Numerade Educator
00:50

Problem 32

Graph each function in the standard viewing window of your calculator, and trace from left to right along a representative portion of the specified interval. Then fill in the blank of the following sentence with either increasing or decreasing.
Over the interval specified, this function is __________.

$$f(x)=x^{2}-2 x ;(1, \infty)$$

AG
Ankit Gupta
Numerade Educator
00:43

Problem 33

Graph each function in the standard viewing window of your calculator, and trace from left to right along a representative portion of the specified interval. Then fill in the blank of the following sentence with either increasing or decreasing.
Over the interval specified, this function is __________.

$$f(x)=2-x^{2} ;(-\infty, 0)$$

AG
Ankit Gupta
Numerade Educator
00:57

Problem 34

Graph each function in the standard viewing window of your calculator, and trace from left to right along a representative portion of the specified interval. Then fill in the blank of the following sentence with either increasing or decreasing.
Over the interval specified, this function is __________.

$$f(x)=|x+1| ;(-\infty,-1)$$

AG
Ankit Gupta
Numerade Educator
01:10

Problem 35

Using visual observation, determine whether each graph is symmetric with respect to the (a) $x$ -axis, (b) $y$ -axis, or (c) origin.
(GRAPH CAN NOT COPY)

AG
Ankit Gupta
Numerade Educator
01:05

Problem 36

Using visual observation, determine whether each graph is symmetric with respect to the (a) $x$ -axis, (b) $y$ -axis, or (c) origin.
(GRAPH CAN NOT COPY)

AG
Ankit Gupta
Numerade Educator
00:56

Problem 37

Using visual observation, determine whether each graph is symmetric with respect to the (a) $x$ -axis, (b) $y$ -axis, or (c) origin.
(GRAPH CAN NOT COPY)

AG
Ankit Gupta
Numerade Educator
01:05

Problem 38

Using visual observation, determine whether each graph is symmetric with respect to the (a) $x$ -axis, (b) $y$ -axis, or (c) origin.
(GRAPH CAN NOT COPY)

AG
Ankit Gupta
Numerade Educator
00:48

Problem 39

Using visual observation, determine whether each graph is symmetric with respect to the (a) $x$ -axis, (b) $y$ -axis, or (c) origin.
(GRAPH CAN NOT COPY)

AG
Ankit Gupta
Numerade Educator
00:55

Problem 40

Using visual observation, determine whether each graph is symmetric with respect to the (a) $x$ -axis, (b) $y$ -axis, or (c) origin.
(GRAPH CAN NOT COPY)

AG
Ankit Gupta
Numerade Educator
00:57

Problem 41

Using visual observation, determine whether each graph is symmetric with respect to the (a) $x$ -axis, (b) $y$ -axis, or (c) origin.
(GRAPH CAN NOT COPY)

AG
Ankit Gupta
Numerade Educator
00:57

Problem 42

Using visual observation, determine whether each graph is symmetric with respect to the (a) $x$ -axis, (b) $y$ -axis, or (c) origin.
(GRAPH CAN NOT COPY)

AG
Ankit Gupta
Numerade Educator
02:50

Problem 43

Complete the left half of the graph of $y=f(x)$ in the figure for each of the following conditions.
(a) $f(-x)=f(x)$
(b) $f(-x)=-f(x)$
(GRAPH CAN NOT COPY)

AG
Ankit Gupta
Numerade Educator
02:34

Problem 44

Complete the right half of the graph of $y=f(x)$ in the figure for each of the following conditions.
(a) $f$ is odd.
(b) $f$ is even.
(GRAPH CAN NOT COPY)

AG
Ankit Gupta
Numerade Educator
00:57

Problem 45

Complete the table, assuming that $f$ is en even function.
$$\begin{array}{c|c|c|c|c|c|c}
x & -3 & -2 & -1 & 1 & 2 & 3 \\
\hline f(x) & 21 & & -25 & & -12 &
\end{array}$$

AG
Ankit Gupta
Numerade Educator
01:19

Problem 46

Complete the table, assuming that $g$ is an odd function.
$$\begin{array}{c|c|c|c|c|c|c|c}
x & -5 & -3 & -2 & 0 & 2 & 3 & 5 \\
\hline g(x) & 13 & & -5 & & & -1 &
\end{array}$$

AG
Ankit Gupta
Numerade Educator
01:10

Problem 47

Based on the ordered pairs seen in each table, make a conjecture about whether the function $f$ is even, odd, or neither even nor odd.
$$\begin{array}{r|r}
x & f(x) \\
\hline-3 & 10 \\
-2 & 5 \\
-1 & 2 \\
0 & 1 \\
1 & 2 \\
2 & 5 \\
3 & 10
\end{array}$$

Breanna Ollech
Breanna Ollech
Numerade Educator
01:03

Problem 48

Based on the ordered pairs seen in each table, make a conjecture about whether the function $f$ is even, odd, or neither even nor odd.
$$\begin{array}{r|r}
x & f(x) \\
\hline-3 & 16 \\
-2 & 5 \\
-1 & 1 \\
0 & -4 \\
1 & 1 \\
2 & 5 \\
3 & 16
\end{array}$$

AG
Ankit Gupta
Numerade Educator
01:02

Problem 49

Based on the ordered pairs seen in each table, make a conjecture about whether the function $f$ is even, odd, or neither even nor odd.
$$\begin{array}{r|r}
x & f(x) \\
\hline-3 & 10 \\
-2 & 5 \\
-1 & 2 \\
0 & 0 \\
1 & -2 \\
2 & -5 \\
3 & -10
\end{array}$$

AG
Ankit Gupta
Numerade Educator
01:07

Problem 50

Based on the ordered pairs seen in each table, make a conjecture about whether the function $f$ is even, odd, or neither even nor odd.
$$\begin{array}{r|r}
x & f(x) \\
\hline-3 & -5 \\
-2 & -4 \\
-1 & -1 \\
0 & 0 \\
1 & 1 \\
2 & 4 \\
3 & 5
\end{array}$$

AG
Ankit Gupta
Numerade Educator
01:00

Problem 51

Based on the ordered pairs seen in each table, make a conjecture about whether the function $f$ is even, odd, or neither even nor odd.
$$\begin{array}{r|r}
x & f(x) \\
\hline-3 & 5 \\
-2 & 4 \\
-1 & 3 \\
0 & 2 \\
1 & 1 \\
2 & 0 \\
3 & -1
\end{array}$$

AG
Ankit Gupta
Numerade Educator
01:00

Problem 52

Based on the ordered pairs seen in each table, make a conjecture about whether the function $f$ is even, odd, or neither even nor odd.
$$\begin{array}{r|r}
x & f(x) \\
\hline-3 & -1 \\
-2 & 0 \\
-1 & 1 \\
0 & 2 \\
1 & 3 \\
2 & 4 \\
3 & 5
\end{array}$$

AG
Ankit Gupta
Numerade Educator
00:54

Problem 53

Each function is either even or odd. Use $f(-x)$ to state which situation applies.
$$f(x)=x^{4}-7 x^{2}+6$$

AG
Ankit Gupta
Numerade Educator
00:57

Problem 54

Each function is either even or odd. Use $f(-x)$ to state which situation applies.
$$f(x)=-2 x^{6}-8 x^{2}$$

AG
Ankit Gupta
Numerade Educator
00:52

Problem 55

Each function is either even or odd. Use $f(-x)$ to state which situation applies.
$$f(x)=3 x^{3}-x$$

AG
Ankit Gupta
Numerade Educator
01:01

Problem 56

Each function is either even or odd. Use $f(-x)$ to state which situation applies.
$$f(x)=-x^{5}+2 x^{3}-3 x$$

AG
Ankit Gupta
Numerade Educator
00:51

Problem 57

Each function is either even or odd. Use $f(-x)$ to state which situation applies.
$$f(x)=x^{6}-4 x^{4}+5$$

AG
Ankit Gupta
Numerade Educator
00:58

Problem 58

Each function is either even or odd. Use $f(-x)$ to state which situation applies.
$$f(x)=8$$

AG
Ankit Gupta
Numerade Educator
00:52

Problem 59

Each function is either even or odd. Use $f(-x)$ to state which situation applies.
$$f(x)=3 x^{5}-x^{3}+7 x$$

AG
Ankit Gupta
Numerade Educator
00:36

Problem 60

Each function is either even or odd. Use $f(-x)$ to state which situation applies.
$$f(x)=x^{3}-4 x$$

AG
Ankit Gupta
Numerade Educator
00:46

Problem 61

Each function is either even or odd. Use $f(-x)$ to state which situation applies.
$$f(x)=|5 x|$$

AG
Ankit Gupta
Numerade Educator
00:42

Problem 62

Each function is either even or odd. Use $f(-x)$ to state which situation applies.
$$f(x)=\sqrt{x^{2}+1}$$

AG
Ankit Gupta
Numerade Educator
00:33

Problem 63

Each function is either even or odd. Use $f(-x)$ to state which situation applies.
$$f(x)=\frac{1}{2 x}$$

AG
Ankit Gupta
Numerade Educator
00:38

Problem 64

Each function is either even or odd. Use $f(-x)$ to state which situation applies.
$$f(x)=4 x-\frac{1}{x}$$

AG
Ankit Gupta
Numerade Educator
00:38

Problem 65

Use the analytic method of Example 3 to determine whether the graph of the given function is symmetric with respect to the $y$ -axis, symmetric with respect to the origin, or neither. Use your calculator and the standard window to support your conclusion.
$$f(x)=-x^{3}+2 x$$

AG
Ankit Gupta
Numerade Educator
00:36

Problem 66

Use the analytic method of Example 3 to determine whether the graph of the given function is symmetric with respect to the $y$ -axis, symmetric with respect to the origin, or neither. Use your calculator and the standard window to support your conclusion.
$$f(x)=x^{5}-2 x^{3}$$

AG
Ankit Gupta
Numerade Educator
00:44

Problem 67

Use the analytic method of Example 3 to determine whether the graph of the given function is symmetric with respect to the $y$ -axis, symmetric with respect to the origin, or neither. Use your calculator and the standard window to support your conclusion.
$$f(x)=0.5 x^{4}-2 x^{2}+1$$

AG
Ankit Gupta
Numerade Educator
01:06

Problem 68

Use the analytic method of Example 3 to determine whether the graph of the given function is symmetric with respect to the $y$ -axis, symmetric with respect to the origin, or neither. Use your calculator and the standard window to support your conclusion.
$$f(x)=0.75 x^{2}+|x|+1$$

AG
Ankit Gupta
Numerade Educator
00:40

Problem 69

Use the analytic method of Example 3 to determine whether the graph of the given function is symmetric with respect to the $y$ -axis, symmetric with respect to the origin, or neither. Use your calculator and the standard window to support your conclusion.
$$f(x)=x^{3}-x+3$$

AG
Ankit Gupta
Numerade Educator
00:33

Problem 70

Use the analytic method of Example 3 to determine whether the graph of the given function is symmetric with respect to the $y$ -axis, symmetric with respect to the origin, or neither. Use your calculator and the standard window to support your conclusion.
$$f(x)=x^{4}-5 x+2$$

AG
Ankit Gupta
Numerade Educator
00:40

Problem 71

Use the analytic method of Example 3 to determine whether the graph of the given function is symmetric with respect to the $y$ -axis, symmetric with respect to the origin, or neither. Use your calculator and the standard window to support your conclusion.
$$f(x)=x^{6}-4 x^{3}$$

AG
Ankit Gupta
Numerade Educator
01:21

Problem 72

Use the analytic method of Example 3 to determine whether the graph of the given function is symmetric with respect to the $y$ -axis, symmetric with respect to the origin, or neither. Use your calculator and the standard window to support your conclusion.
$$f(x)=x^{3}-3 x$$

AG
Ankit Gupta
Numerade Educator
00:57

Problem 73

Use the analytic method of Example 3 to determine whether the graph of the given function is symmetric with respect to the $y$ -axis, symmetric with respect to the origin, or neither. Use your calculator and the standard window to support your conclusion.
$$f(x)=-6$$

AG
Ankit Gupta
Numerade Educator
00:41

Problem 74

Use the analytic method of Example 3 to determine whether the graph of the given function is symmetric with respect to the $y$ -axis, symmetric with respect to the origin, or neither. Use your calculator and the standard window to support your conclusion.
$$f(x)=|-x|$$

AG
Ankit Gupta
Numerade Educator
00:38

Problem 75

Use the analytic method of Example 3 to determine whether the graph of the given function is symmetric with respect to the $y$ -axis, symmetric with respect to the origin, or neither. Use your calculator and the standard window to support your conclusion.
$$f(x)=\frac{1}{4 x^{3}}$$

AG
Ankit Gupta
Numerade Educator
00:25

Problem 76

Use the analytic method of Example 3 to determine whether the graph of the given function is symmetric with respect to the $y$ -axis, symmetric with respect to the origin, or neither. Use your calculator and the standard window to support your conclusion.
$$f(x)=\sqrt{x^{2}}$$

AG
Ankit Gupta
Numerade Educator